Some bounds for the degree of commutativity of a p-group of maximal class
1995 ◽
Vol 51
(3)
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pp. 353-367
Keyword(s):
In this paper we obtain several lower bounds for the degree of commutativity of a p-group of maximal class of order pm. All the bounds known up to now involve the prime p and are almost useless for small m. We introduce a new invariant b which is related with the commutator structure of the group G and get a bound depending only on b and m, not on p. As a consequence, we bound the derived length of G and the nilpotency class of a certain maximal subgroup in terms of b. On the other hand, we also generalise some results of Blackburn. Examples are given in order to check the sharpness of the bounds.
1977 ◽
Vol 29
(2)
◽
pp. 333-348
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Keyword(s):
1972 ◽
Vol 7
(3)
◽
pp. 391-405
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1992 ◽
Vol 46
(3)
◽
pp. 497-507
Keyword(s):
1999 ◽
Vol 173
◽
pp. 249-254
Keyword(s):
1969 ◽
Vol 27
◽
pp. 6-7
Keyword(s):
1980 ◽
Vol 38
◽
pp. 30-33
2005 ◽
Vol 19
(3)
◽
pp. 129-132
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Keyword(s):